Erroneous Worldwide Practice
I will enumerate the irrational and erroneous worldwide practice so that in this age of electronic digital computer and Microsoft Excel, the paradigm of exactitude can be realized in the engineering and structural community. The world have been buried and brainwashed by the tons of reference materials which were invented before the age of computers to enable an approximate analysis to be considered as practical because of time constraints. This practice of expediency and compliance was continued with the invention of finite-element methods on a fixed orthogonal XYZ axes in a 3D analysis. The copying of reference materials became a habit of world experts in employing the established principles of Euler’s, Hooke’s law and Pythagorean Theorem. Unbeknownst to these experts are the hundreds of integral calculus equations required to satisfy these principles using basic mathematics and physics. These equations however must be derived from known principles in science. Laziness on the part of world experts is preferred and copying each other became a normal routine. I will now enumerate the reasons copying existing reference materials in structural engineering analysis is simply wrong. My reference is my reinforced concrete column software for a given composite circular and rectangular section.
1. The column capacity axis to determine the minimum yield capacity of a section was never implemented by the current method. Reliance was made on the finite-element method on fixed orthogonal XYZ axes. On a rectangle, the horizontal axis is the column capacity axis. Intuition, however dictates that the diagonal of a rectangle must be the column capacity axis since basic mathematics and physics require the rotation of orthogonal XYZ axes. Therefore the horizontal axis must be rotated for the minimum column capacity axis at the diagonal of a rectangle. An angle of rotation must therefore be introduced as a variable to obtain the minimum column yield capacity of a rectangular section. Also, in analytic geometry the straight line equations are given and therefore a rectangle with parallel sides can be derived for an analytical solution. Current practice does not rotate the orthogonal XYZ axes to satisfy the requirement of minimum column yield capacity at the diagonal of a rectangle nor derive the rectangular equation from analytic geometry for an analytical solution. They continue to employ the standard interaction formula to estimate the minimum column yield capacity with the column capacity axis at the horizontal. This is a glaring error in the non-rotation of the orthogonal XYZ axes because doing so allows anybody to employ basic mathematics and physics as required in the analysis of a structural problem without justification. This condition can readily be seen in a rectangular section where the diagonal represents the column capacity axis for developing the minimum column yield capacity. There is an appreciable error when the current world method consider the horizontal axis as the column capacity axis. A reduction of minimum column yield capacity is exposed by the exact method.
2. The coordinates of the reinforcing bars referred at the center of the circular or rectangular section must be mathematically derived and included in the analysis for an analytical solution to be verified by Microsoft Excel in a column software. No software in the world except that of the undersigned has numerically confirmed the hundreds of integral calculus equations derived from Euler’s, Hooke’s law and Pythagorean Theorem. Of course, current world method does not do this procedure because they do not derive the hundreds of integral equations required by the established principles. They continued copying existing reference materials from books as well as relevant codes of practice when analyzing structural problem.
3. Current method uses one pivot point (for concrete alone) for concrete stress diagram accepted universally from breakage of concrete cylinders and cubes. Parabola’s equation and its properties are known in analytic geometry and can be utilized analytically. Current method uses the rectangular stress block and copied universally to satisfy Hooke’s Law. This however, is a mediocre approach and statically cannot be satisfied and yet copied universally. The true method of an exact analysis dictates that two pivot points (one for concrete and the other for steel) must be employed since the stresses for both materials at yield must be held in a free body diagram. This procedure is never been done in world practice and existing column software is therefore irrational and simply wrong. For steel alone, one pivot point is required to maintain the yield capacity in the free body diagram.
4. The resultant bending moment in the Euler’s principle is M2 = Mx2 + My2. The resultant bending moment M per Euler’s principle is the square root of this equation for M. This is not done at the diagonal of a rectangle where the column capacity axis will give the minimum column yield capacity. The measurements in the laboratory from modelling do not reconcile with the hundreds of integral calculus equations for minimum column yield capacity. Therefore, wrong conclusions are arrived at by the researchers.
5. The by-product of a column software is an envelope of minimum column yield capacity and this envelope is bounded by the definition of a short and long column category. A short column is that in which the entire section is at compression. A long column is that in which the section is now in tension and compression. This envelope depends only on the strength of materials used and the values are constants. The horizontal axis in this graph represent the resultant bending moment and the vertical axis represents the axial load. Since the current practice uses the horizontal axis as the column capacity axis, the values represented cannot be used for the calculation of design safety factor. Guesswork and factor of ignorance can easily result from this procedure. The correct procedure is to determine the resultant external load for any locality and plot the value on this envelope such that the external load is inside the envelope for safety in design because failure is impossible to occur if the resultant external load is inside this envelope. The real factor of safety in design can now be determined by the position of this external load inside this envelope. When the external load is plotted inside this envelope, the real factor of safety against bending moment as well as the real factor of safety against axial load are determined. A point in the boundary of this envelope represents the minimum column yield capacity of a composite circular or rectangular section. Application of the given section is automatically determined whether short or long column when the external load is plotted inside this envelope. This procedure is not done in the current world practice.
6. Current software employing the equations in reference materials are therefore irrational and inaccurate. Software in use refer to approximate methods supported by tons of reference materials. Correct software is therefore not done when referring to these antiquated literature. Use the power of Microsoft Excel to program all derived equations and hence numerically validate all these derived equations. Alas, world experts have been too lazy to perform this procedure because copying others who are also wrong is easier for expediency and compliance. For their information, the minimum column capacity axis for a rectangular section is thru the diagonal. For a composite circular section, the column capacity axis is a diameter between any 2 reinforcing bars.
The free body diagrams representing all the variables in a circular and rectangular section are shown in a book entitled “Analytical Method in Reinforced Concrete”. The integral equations derived from established principles of Euler’s, Hooke’s Law and Pythagorean Theorem are listed therein. The exact and correct methodology in structural analysis is numerically confirmed using Microsoft Excel to program all the derived equations using 2 pivot points instead of the current one pivot for concrete alone. I am keeping a copy of the only column software that was ignored internationally in 1996 as a proof of the exact method. This software was advertised in an ASCE structural magazine and registered in the Library of Congress in that same year but was ignored by the structural community since reference materials on approximate methods abounds in literature.
You may visit my engineering website at www.ramonjarquio.com for more details should you be interested in doing the right thing or risk deliberate ignorance now that we are in the age of electronic digital computers. The tons of literature in approximate methods should be relegated to posterity and basic mathematics and physics can now be implemented and computers can numerically confirm validity of derived equations in structural mechanics. A new paradigm of exactitude is mandatory and many technical articles (28 previously) I wrote in Linkedin.com can be read and digested. Alternatively, my 3 published technical books can be referred to for the derived equations for 1 pivot point and 2 pivot points as required.
Prepared by: Ramon V. Jarquio, P.E.
Email: [email protected]